On stability of outer inverses

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The paper is concerned with stability properties of bounded outer inverses for bounded operators on Banach spaces. We investigate the effect of perturbations of subspaces generating outer inverses for a given operator. We prove that the convergence of respective gaps between subspaces implies the convergence in the norm of outer inverses generated by these subspaces. The notion of outer inverses is illustrated by an example which gives the form of outer inverses for an arbitrary matrix.